Our deadline is January 1st. Technically, you could submit an application at 11:59 PM on January 1st and meet the deadline.
The Common App system builds in a grace period in case there are technical problems, but I strongly encourage you to hit submit before that final hour. There is obviously a lot of traffic on the Common App servers on that final day and while I'm sure they can handle it, I can imagine the panic you'd feel if your internet connection cut out during those final moments of deadline day.
In addition, if you have questions for the Common App people, I imagine you'll get a faster response to a help ticket submission if you are asking during normal business hours. If you submit a help request at 10 PM, you'll probably be one of many doing the same thing and therefore won't hear back for a little while.
I know this is an extremely stressful time. I imagine there is some freaking out going on. Do yourself a favor and made a personal deadline that's before the official one.
Good luck! As always, you can post questions here and I'll do my best to answer them quickly!
CavDog knows you're probably sick of sitting in front of the computer right now